1. Field of the Invention
The present invention relates to a control system to control a position or position related quantity such as velocity or acceleration of an object, a lithographic apparatus including a control system and a method for increasing the bandwidth of a position control system.
2. Background Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In known lithographic apparatus, control systems are used to control the position or position related quantities such as velocity or acceleration of an object. Such a control system may be used to control the position of a movable object with high accuracy, for instance the servo control system of a substrate support or a patterning device support. Similarly, a control system may be used to control the velocity or the acceleration of the object. Because velocity, acceleration and position of an object are closely related, velocity being the time integral of acceleration and position being the time integral of velocity, all three can be regarded as position related quantities of the object. For that reason, the term ‘position control’ as used herein is intended to cover cases where velocity or acceleration or other position related quantities are the controlled variables.
In other applications, a control system may be used to stabilize the position of a substantially stationary object. Such control system is often referred to as an active damping system. In an active damping system, usually the velocity is the actual controlled variable.
An example of such substantially stationary object is a projection system. Such a projection system includes a number of lens elements and/or mirrors and is held, during projection, in the optical path between a patterning device and substrate. The patterning device and substrate are positioned with respect to the projection system to obtain an optimal imaging quality. However due to vibrations and other movements in the lithographic apparatus, movements of the projection system may occur. In order to suppress these movements it has been proposed to provide an active damping system to minimize movements, velocities, and/or accelerations of the projection system.
A known embodiment of such control system includes an acceleration sensor to measure accelerations of the object, a controller to provide a control signal on the basis of the measured acceleration and an actuator to provide a reaction force to counteract the acceleration and therewith the movement of the object. The actuator is connected to the object and to a reaction mass. In a known embodiment, the mass is a free mass which means that it is only connected to the actuator. As a result, the reaction force is not exerted on for instance a frame. Alternatively, the reaction force could be exerted on a reaction frame or the like.
A drawback of the known embodiment is that the control system may easily become unstable as for higher frequencies the gain of the transfer function of the system may increase while the phase crosses −180 degrees. The increasing gain is for instance a result of lens elements which are mounted with limited stiffness in the projection system, and become decoupled from the housing for frequencies above its resonance frequency. Applying the same force at a higher frequency therefore leads to a higher acceleration, because less mass is actuated when lens elements are decoupled. Therefore, the gain may increase for higher frequencies. The combination of high or even increasing gains for high frequencies increases the risk on an unstable system.
In many control system a first or higher order low-pass filter is applied to dampen the high gains for higher frequencies to avoid instability of the system. However, for the above-described known active damping system the application of such a first of higher order low-pass filter may not be possible since the damping of the gains also implies a phase lag, therewith generally decreasing the frequency at which −180 degrees is crossed and increasing the chance on instability. As a result, it may be difficult or even impossible to position the cut-off frequency of the first or higher order filter such that a stable system is obtained.
Generally, it is not desired to increase the bandwidth of a position control system, the bandwidth being defined as the first frequency where the gain of the open loop transfer function drops below one (0 dB). At the same time it is desired to have a stable system.